If 2 angles are both vertical and supplementary, then the angles are

Given :

A sequence of numbers begins at 400.

To Find :

If the pattern increases by consecutive multiples of 5 starting with 5, then find the next 3 numbers in the sequence 400, ___, ___, ___ .

Solution :

This is the a question of arithmetic progression .

The first term is , a = 400 .

Now , it is given that the next numbers increase by the multiples of 5 starting with 5 .

So , common difference is , d = 5 .

Now , we know , [tex]n^{th}[/tex] number in A.P is given by :

[tex]a_n=a+(n-1)d[/tex]

Putting value of n = 2 , 3 , 4 .

We get :

[tex]a_2=a+(2-1)d=400+5=405\\\\a_3=a+(3-1)d = 400 + (5\times 2) = 410\\\\a_4=a+(4-1)d = 400 +(5\times 3)=415[/tex]

Therefore , the next 3 numbers in the sequence is 400 , 405 , 410 , 415 .

Hence , this is the required solution .

Answer:

Taking LHS

=1 by cos theta- cos theta

= (1- cos²0)/ cos0

= sin²0/ cos0 ( because 1-cos²0 is also equals to sin²0)

=RHS hence proved

Answer:

Step-by-step explanation:

Let theta be β.

So,

[tex]sec\beta - cos\beta = \frac{sin^2\beta }{cos\beta } \\=>\frac{1}{cos\beta } - cos\beta = \frac{1 - cos^2\beta }{cos\beta } \\=>\frac{1 - cos^2}{cos\beta } = \frac{1 - cos^2\beta }{cos\beta }[/tex]

Here , identity used = [tex]sin^2\beta + cos^2\beta = 1[/tex]

Answer:

Variable cost $3.79 ; fixed cost = $2185.47

Step-by-step explanation:

Given the data :

Rental return(x) :

2300

2500

2700

2900

3600

4900

5400

5300

4600

3800

2100

2500

Car wash cost :

10200

12700

11000

13100

15400

21700

21400

20200

22000

18700

9900

11400

Using the online regression calculator :

The obtained regression equation is :

ŷ = 3.79X + 2185.47

Comparing the obtained result with the general form of the equation:

y = mx + c

Where m = gradient or slope whose value gives the variation in cost per rental return (x)

c = intercept, which is constant or fixed, it is the value where the regression line crosses the y axis, hence, it corresponds to the fixed cost.

Hence,

The variable cost per rental return(m)

mx = 3.79x

m = $3.79

The fixed cost :

c = $2185.47

Answer:

B

Step-by-step explanation:

B is true because 0.2 x 10 = 2

Answer:

[See Below]

Step-by-step explanation:

✦ The pattern is y ÷ 8. (So just divided by 8 each time.)

  ✧ 512 ÷ 8 = 64

  ✧ 64 ÷ 8 = 8

  ✧ 8 ÷ 8 = 1

  ✧ 1 ÷ 8 = 0.125

  ✧ 0.125 ÷ 8 = 0.015625

✦ So then the next values would be:  

  ✧ 8⁰ = 1

  ✧ 8⁻¹ = 0.125

  ✧ 8⁻² = 0.015625

~Hope this helps Mate. If you need anything feel free to message me.

Hey there! I'm happy to help!

To find the volume of a cylinder, you multiply the base by the height.

First, we find the base. The base is a circle. To find the area of a circle, you square the radius and multiply it by pi (we will use 3.14). The radius is half the diameter.

6.5/2=3.25

We square this.

3.25²=10.5625

And multiply by 3.14

10.5625(3.14)=33.16625

Now we multiply this by the height.

33.16625(12)=397.995

Therefore, the volume of this silo is 397.995 cubic meters.

Have a wonderful day! :D

Answer:

It is a negative 1.75. (-1.75)

Answer:

2f(x); g(x) = 10/x

Step-by-step explanation:

The second option on edge

The new equation is, g(x) =2f(x), g(x) =10/x. Option B is correct.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

Given data in problem is;

a = F/M

f(x) = 5/x

We have to examine each option given and observe the graph for the function we got;

g(x) = 2f(x)

Substitute the values we get;

g(x) =  2×(5/x)

g(x)=10/x

The new equation is, g(x) =2f(x), g(x) =10/x.

Hence, option B is correct.

The complete question and graph are attached below.

To learn more about the graph, refer to the link;

https://brainly.com/question/14375099

#SPJ2

Answer:

111100 base 2

Step-by-step explanation:

The conversion of 60 base 10 to base 2

When converting a number from base 10 to base 2, the following steps are taken:

a) The number in base 10 is divided by 2 and the remainder is recorded, this continues until the remainder is less than 2.

b) The remainder from the bottom to the top are arranged so as to get the representation of the number in base 2.

60 base 10 to base 2

60 ÷ 2       =       30  remainder  0

30 ÷ 2       =        15 remainder   0

15 ÷ 2       =         7   remainder   1

7 ÷ 2        =          3  remainder   1

3 ÷ 2        =          1   remainder   1

1 ÷ 2         =          0  remainder   1

The remainder from bottom to top is 111100 base 2.

(60)₁₀ = (111100)₂

Answer:

8x²-2x-5

Step-by-step explanation:

2x²-(5+2x)+6x²

2x²-5-2x+6x²

2x²+6x²-2x-5

8x²-2x-5

Hope this helps ;) ❤❤❤

Answer:

[tex]8 {x}^{2} - 2x - 5[/tex]

Step-by-step explanation:

[tex]2 {x}^{2} - (5 + 2x) + 6 {x}^{2} [/tex]

[tex]2 {x}^{2} - 5 - 2x + 6 {x}^{2} [/tex]

[tex]8 {x}^{2} - 2x - 5[/tex]

Answer:

5 + 3a

Step-by-step explanation:

The expression is:

5 + 3a

Answer:

Step-by-step explanation:

The question lacks the required diagram. Find the diagram attached.

From the diagram it can be seen that the line is parallel to the y axis, hence we are going to locate each endpoints on the y axis.

The lower end point is on 2units while the upper end point is on 9 units both on the y axis. The distance between this two points will be the difference between the end point values i.e 9-2 = 7 units.

Hence the distance between the two points shown  is 7 units

Answer: The length is 88 yards  and the width is 10 yards. Look into the steps for more information.

Step-by-step explanation:

The length is 12 yards less than 10 times the width so we can represent that by the equation  L = 10w - 12  

And the area is 880  so the width times the length has to equal 880. the width is w and the length is 10w -12

w( 10w -12 ) = 880   solve for w

10w^2 - 12w  = 880    subtract 880 from both sides

              -880   -880

10w^2 - 12w - 880 = 0     They share the same factors so dive each side by 2

5w^2 - 6w^2 - 440 = 0  

a= 5     b = -6  and c=-440

The quadratic formula says that x= -b ± [tex]\sqrt{b^2- 4ac} / 2a[/tex]  

   x= 6 ±[tex]\sqrt{8836} / 5[/tex]  

x= 6 ± 94  /10

x= 100 /10

x = 10  

In this case the width is 10 yards.

The length is 12 less than 10 times the width .

So   L  = 10(10) - 12

   L =  100- 12

  l = 88  

So the length is 88

The required length and width are 229 and 27 yards.

It is required to find the dimension of rectangle.

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

Given:

A=l*w

w=width

10w-12=length

According to given question we have,

6183=(10w-12)(w)

6183=10[tex]w^{2}[/tex]-14w

9[tex]w^{2}[/tex]-14w-6183=0

By simplify we get,

(9w+229)(w-27)=0

w-27=0

w=27 yards

l=9*27-14=229 yards

Therefore, the required length and width are 229 and 27 yards.

Learn more details about rectangle here:

https://brainly.com/question/15019502

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Answer:

x = 3*cos(t) - 2  

y = 3*sin(t) + 2  

Step-by-step explanation:

The equation for a circle of radius 3 and centered at the point ( h , k )           (  -2 , 2 ) is:

( x - h )²  +  (  y  - k )²  = r²

In this particular case

h = - 2   k = 2    and  r = 3

Then to parametrizace the equation

x  = r* cos(t) +  h

y = r*sin(t)  + k

x =  3*cos(t) + (- 2)       ⇒   x = 3*cos(t) - 2    

y = 3 *sin(t) + (2)          ⇒   y = 3*sin(t) + 2

Now :

when t = 0   x should be  1

Then   x = 3 cos(0) - 2      x  = 3 - 2        x  = 1

and t = 0   y should be 2

Then   y = 3*sin(t) + 2    ⇒  y =  3*sin(0) + 2       y  =  2

Answer: G.

Step-by-step explanation: you should divide both sides by 3. 3 divided by 3 is 0, and -12 divided by 3 is -4. therefore, your answer is (0,-4)

Answer: G (0,-4)

Step-by-step explanation:

You can use this website called "Desmos Graphing Calculator." The answer is G.(0,-4). It helps me a lot with graphing and graphing linear equations.

Answer:

4,1

Step-by-step explanation:

Hi there! :)

Answer:

[tex]\huge\boxed{y = -7/2x + 4}[/tex]

Given equation:

y = 2/7x - 5

A perpendicular line will have a slope that is the opposite reciprocal, therefore:

2/7 --> -7/2

Substitute the x and y coordinates of the point given to write an equation in slope-intercept form:

(-3) = -7/2(2) + b

Simplify:

-3 = -7 + b

-3 + 7 = b

b = 4

Rewrite the equation:

y = -7/2x + 4

Answer:

-21.5

Step-by-step explanation:

-8x+23-22+9=182

-8x+1+9=182

-8x+10=182

     -10   -10

-8x=172

x=172÷-8

x=-21.5

-21.5 IS THE ANSWER

Answer:

5+a/a-1

Step-by-step explanation:

3+a+2/a+2-3=5+a/a-1

Answer:

y=50

Step-by-step explanation:

look at photo attached

Answer:

y=50

Step-by-step explanation:

on edge2021

Answer:

about $57.42

Step-by-step explanation:

we know how many miles they drove in all (510) and how many miles they can drive per gallon (23)

we need to find out how many gallons of gas they used by dividing the total number of miles they drove (510) by the number of miles per gallon (23) which is about 22.17

510 ÷ 23 = 22.17

we then need to find out how much money they spent on the total number of gallons of gas they purchased by multiplying 22.17 by the amount of money for one gallon of gas ($2.59)

22.17 × 2.59 = $57.42

Answer:

[tex]41\frac{247}{500}[/tex]

Step-by-step explanation:

41.494  

= [tex]41\frac{494}{1000}[/tex]

to simplify the fraction 494 /1000, we have to find and divide both numerator and denominator by the their highest common factor

494 = 2 x 13 x 19

1000 = 2 x 2 x 2 x 5 x 5 x 5

comparing the two, we can see that that the only common factor that both numbers share is 2, hence we divide both numerator and denominator by 2

41 494/1000

= [tex]41\frac{494}{1000}[/tex]

= [tex]41\frac{494/2}{1000/2}[/tex]

= [tex]41\frac{247}{500}[/tex]

Answer:

$12750

Step-by-step explanation:

Initial price = $8500

Markup = 150%

Markup amount:

Selling price would be:

Answer:

36 girls signed up

Step-by-step explanation:

1. Create a ratio for boys to girls: 8:6

2. Multiply 8 * 6 to get 48 (amount of boys who signed up.)

Whatever we do one on side we do to the other, so multiply the girls by 6.

6 * 6 = 36

48:36 = 8:6

these ratios are proportional

Answer: y = 7/3 - (4/3)*x

Step-by-step explanation:

First, let's write our line in the notation:

y = f(x)

So we must isolate y in the equation:

4x + 3y = 12

3y = 12 - 4x

y = 12/3 - (4/3)*x = 4 - (4/3)*x

Now, we have two translations, one horizontal and one vertical.

Let's define them in general cases:

Horizontal translation.

When we have y = f(x) and we want to do a horizontal translation of A units to the right (A positive) we have:

y = g(x) = f(x - A)

So we replace our variable x by x - A.

Vertical translation.

When we have y = f(x) and we want to do a horizontal translation of A units up (A positive) we have:

y = g(x) = f(x) + A.

Then in this case we have:

y = f(x) = 4 - (4/3)*x

then, the horizontal translation of 1 unit to the right is:

y = f(x - 1) = 4 - (4/3)*(x - 1)

And the translation of 3 units down (a vertical translation) is:

y = f(x - 1) - 3 = 4 - (4/3)*(x - 1) - 3  = 1 + 4/3 - (4/3)*x

y = 7/3 - (4/3)*x

This equation represents the new line.